Abstract
We consider element-by-element Schur complement approximations for indefinite and general nonsymmetric matrices of two-by-two block form, as arising in finite element discretized systems of PDEs. The paper provides some analysis of the so-obtained approximation and attempts to quantify the quality of the underlying two-by-two matrix splitting in a way similar to that used for symmetric positive definite matrices. The quality of the approximation is illustrated numerically.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Axelsson, O.: Iterative Solution Methods. Oxford University Press, Oxford (1994)
Axelsson, O., Blaheta, R., Neytcheva, M.: Preconditioning for boundary value problems using elementwise Schur complements. SIMAX 31, 767–789 (2009)
Braess, D.: Finite Elements, 2nd edn. Cambridge University Press, Cambridge (2001)
Davis, T.A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Transactions on Math. Software 30, 165–195 (2004)
de Niet, A.C., Wubs, F.W.: Two preconditioners for saddle point problems in fluid flows. Int. J. Numer. Meth. Fluids 54, 355–377 (2007)
Do-Quang, M., Amberg, G.: The splash of a ball hitting a liquid surface: Numerical simulation of the influence of wetting. Journal Physic of Fluid (2008) (accepted)
femLego (Numerical simulation by symbolic computation), http://www.mech.kth.se/~gustava/femLego
Kraus, J.: Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Num. Lin. Alg. Appl. 13, 49–70 (2006)
Neytcheva, M., Bängtsson, E.: Preconditioning of nonsymmetric saddle point systems as arising in modelling of visco-elastic problems. ETNA 29, 193–211 (2008)
Villanueva, W., Amberg, G.: Some generic Capillary-driven flows. Int. J. of Multiphase Flow 32, 1072–1086 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Neytcheva, M., Do-Quang, M., Xin, H. (2010). Element-by-Element Schur Complement Approximations for General Nonsymmetric Matrices of Two-by-Two Block Form. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-12535-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12534-8
Online ISBN: 978-3-642-12535-5
eBook Packages: Computer ScienceComputer Science (R0)